⚙️ Algorithm Complexity | Structured Learning Notes

This repository is a practical, execution focused guide to mastering algorithm complexity, designed to develop interview ready intuition, not memorized definitions. The goal is to understand how time and space grow as input scales, and reason confidently about performance trade offs in real code.

It’s meant to be visited repeatedly: to check progress, refresh intuition, and identify the next concept to master.

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What You’ll Learn

• What complexity actually measures (beyond Big-O symbols)
• How to analyze time and space from real code
• How recursion, loops, and data structures affect growth
• How to reason about trade-offs in interviews and production systems

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Learning Roadmap (Top → Bottom)

01. Intuition & Meaning
    ↓
02. Time Complexity
    ↓
03. Space Complexity
    ↓
04. Code → Complexity Mapping
    ↓
05. Trade-offs & Interview Reasoning

Each step builds on the previous one don’t skip.

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Repository Structure

Complexity/
│
├── 01_intuition/                   # What complexity means & why it matters
│   ├── why_complexity_matters.md
│   └── growth_visuals.md
│
├── 02_time_complexity/             # How runtime grows
│   ├── constant_log_linear.py
│   ├── nested_loops.py
│   ├── recursion_examples.py
│   └── amortized_examples.py
│
├── 03_space_complexity/            # How memory grows
│   ├── input_vs_auxiliary.py
│   ├── recursion_stack.py
│   └── in_place_vs_extra_space.py
│
├── 04_code_to_complexity/          # Analyze unknown code
│   ├── analyze_given_code.md
│   ├── brute_vs_optimized.py
│   └── complexity_annotations.py
│
├── 05_tradeoffs/                   # Decision-making & interviews
│   ├── time_vs_space.md
│   └── real_interview_questions.md
│
└── README.md

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How to Use This Repository

• Start with 01_intuition
• Don’t move forward until you can explain the topic in your own words
• Every example should answer: “What grows when input grows?”
• Use this alongside problem solving platforms (LeetCode, DSA practice)

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Visual Guide to Complexity

Operations
^
|                   /  -> O(2^n)   < Horrible >
|                  /
|                 /
|                /  -> O(n^2)   < Horrible >
|               /
|              /
|             /         
|            /
|           /  -> O(n log n) < Bad >
|          /
|         /
|        /
|       /
|      /   -> O(n)  < Fair >
|     /
|    /
|   /   -> O(log n)  < Good >
|  /
| /   -> O(1)  < Best >
+--------------------------------------------------> Elements

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Progress Check (Self-Evaluation)

• Recognize Big-O → Early
• Explain complexity in words → Learning
• Predict complexity from code → Interview-ready

Advanced topics (strings, arrays, patterns) should be tackled only after building solid complexity intuition.

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Purpose

This repository exists to build a mental framework that makes future topics DSA, SQL performance, system design faster and easier to learn.

Master complexity once. Everything else compounds.

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